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Q.
Which of the following statements is correct?
Gravitation
Solution:
Acceleration due to gravity at a altitude $h$ above the earths surface is
$g_{h} = \frac{gR^{2}_{E}}{\left(R_{E}+h\right)^{2}} \quad\ldots \left(i\right)$
where $g$ is the acceleration due to gravity on the earths surface and $R_E$ is the radius of the earth.
$Eq.\, (i)$ shows that acceleration due to gravity decreases with increasing altitude.
Acceleration due to gravity at a depth d below the earths surface is
$g_{d} = g\left(1-\frac{d}{R_{E}}\right) \quad\ldots \left(ii\right)$
$Eq.\, (ii)$ shows that acceleration due to gravity decreases with increasing depth.
Acceleration due to gravity at latitude $\lambda$
$g_{\lambda} = g-R_{E}\omega^{2}\,cos^{2}\lambda \quad\ldots \left(ii\right)$
where $\omega$ is the angular speed of rotation of the earth.
$Eq. \,(iii)$ shows that acceleration due to gravity increases with increasing latitude.
Acceleration due to gravity of body of mass $m$ is placed on the earths surface is
$g = \frac{GM_{E}}{R^{2}_{E}} \quad\ldots\left(iv\right)$
$Eq. \,(iv)$ shows that acceleration due to gravity is independent of the mass of the body but it depends upon the mass of the earth.